Consider the following set of ordered pairs. egin{tabular}{lllrlr} ( mathbf{x} ) & 3 & 3 & 1 & 3 & 4 \ hline ( mathbf{y} ) & 1 & 1 & -2 & 2 & 5 end{tabular} Calculate the coefficient of determination and test its significance using ( alpha=0.05 ). Click the icon to view a partial ANOVA table. Click the icon to view a partial table of critical F-scores with 0.05 in the right tail of the distribution. Calculate the coefficient of determination. ( mathrm{R}^{2}= ) (Round to three decimal places as needed.) AREA IN THE RIGHT TAIL OF DISTRIBUTION ( =0.05 ) egin{tabular}{rrrrrr} ( oldsymbol{D}_{2} ) & ( mathbf{1} ) & ( mathbf{2} ) & ( mathbf{3} ) & ( mathbf{4} ) & multicolumn{1}{c}{( mathbf{5} )} \ ( mathbf{1} ) & 161.448 & 199.500 & 215.707 & 224.583 & 230.162 \ ( mathbf{2} ) & 18.513 & 19.000 & 19.164 & 19.247 & 19.296 \ ( mathbf{3} ) & 10.128 & 9.552 & 9.277 & 9.117 & 9.013 \ ( mathbf{4} ) & 7.709 & 6.944 & 6.591 & 6.388 & 6.256 \ ( mathbf{5} ) & 6.608 & 5.786 & 5.409 & 5.192 & 5.050 \ ( mathbf{6} ) & 5.987 & 5.143 & 4.757 & 4.534 & 4.387 \ ( mathbf{7} ) & 5.591 & 4.737 & 4.347 & 4.120 & 3.972 \ ( mathbf{8} ) & 5.318 & 4.459 & 4.066 & 3.838 & 3.687 \ ( mathbf{9} ) & 5.117 & 4.256 & 3.863 & 3.633 & 3.482 \ ( mathbf{1 0} ) & 4.965 & 4.103 & 3.708 & 3.478 & 3.326 \ & ( mathbf{1} ) & ( mathbf{2} ) & ( mathbf{3} ) & ( mathbf{4} ) & ( mathbf{5} ) \ & & & & & ( D_{1} ) end{tabular} ( egin{array}{ccc}6 & 7 & 8 \ 233.986 & 236.768 & 238.883 \ 19.330 & 19.353 & 19.371 \ 8.941 & 8.887 & 8.845 \ 6.163 & 6.094 & 6.041 \ 4.950 & 4.876 & 4.818 \ 4.284 & 4.207 & 4.147 \ 3.866 & 3.787 & 3.726 \ 3.581 & 3.500 & 3.438 \ 3.374 & 3.293 & 3.230 \ 3.217 & 3.135 & 3.072 \ 6 & 7 & 8end{array} ) ( egin{array}{cc}9 & 10 \ 240.543 & 241.882 \ 19.385 & 19.396 \ 8.812 & 8.786 \ 5.999 & 5.964 \ 4.772 & 4.735 \ 4.099 & 4.060 \ 3.677 & 3.637 \ 3.388 & 3.347 \ 3.179 & 3.137 \ 3.020 & 2.978 \ 9 & 10end{array} ) Partial ANOVA egin{tabular}{cccc|} & multicolumn{3}{c|}{ ANOVA } \ & d.f. & SS & MS \ Regression & 1 & 22.533 \ Error & 3 & 2.667 \ Total & 4 & 25.2 \ hline end{tabular}
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From the given ANOVA table, we have SSR = 22.533 and SST = 25.2. R^2 = 22.533 / 25.2 = 0.894 (rounded to three decimal places) Show more…
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Consider the following set of ordered pairs Calculate the coefficient of determination and test its significance using α = 0.05. Calculate the coefficient of determination R² = (Round to three decimal places as needed) Determine the null and alternative hypotheses. Choose the correct answer below: A. H₀: ρ² = 0, H₁: ρ² > 0 B. H₀: ρ² > 0, H₁: ρ² = 0 C. H₀: ρ² ≥ 0, H₁: ρ² < 0 D. H₀: ρ² < 0, H₁: ρ² ≥ 0 Determine the critical F-score, Fα (Round to three decimal places as needed) Partial ANOVA Calculate the score for this test, F = (Round three decimal places as needed) ANOVA Regression SS: 2.667 Error SS: 0.083 Total SS: 2.750 Determine the correct conclusion. Choose the correct answer below: A. Do not reject H₀; There appears to be relationship between x and y B. Do not reject H₀; There does not appear to be relationship between x and y C. Reject H₀; There does not appear to be relationship between x and y D. Reject H₀; There appears to be relationship between x and y
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The ANOVA summary table for an experiment with six groups with five values in each group is shown to the right. Complete parts (a) through (d) below. Degrees of Freedom | Sum of Squares | Mean Square (Variance) | Source ------------------ | -------------- | ---------------------- | ------ c - 1 = 5 | SSA = 450 | MSA = 90 | Among groups n - c = 24 | SSW = 720 | MSW = 30 | Within groups n - 1 = 29 | SST = 1170 | | Total Find the test statistic: FSTAT = 3 (Round to two decimal places as needed) Determine the critical value: F̑́ = 2.62 (Round to two decimal places as needed) What is your statistical decision? Reject H0. There is sufficient evidence to conclude that there is a difference in the population means of the groups. At the 0.05 level of significance, what is the upper-tail critical value from the Studentized range distribution? Q̑́ = 4.37 (Round to two decimal places as needed) To perform the Tukey-Kramer procedure, what is the critical range? Critical range = 12.360 (Round to three decimal places as needed)
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